Apparatus, systems and methods for generating voltage excitation waveforms

ABSTRACT

A method described herein includes describing a load current with a discrete time function. The method includes using a first frequency and a second frequency to provide an approximation of the described load current, wherein a transform applied to the discrete time function identifies the first frequency and the second frequency. The method includes estimating a loop inductance and a loop resistance of a wire loop by exciting a transmit circuit with a voltage reference step waveform, wherein the transmit circuit includes the wire loop. The method includes scaling the approximated load current to a level sufficient to generate a minimum receive voltage signal in a receiver at a first distance between the wire loop and the receiver. The method includes generating a first voltage signal using the scaled load current, estimated loop inductance, and estimated loop resistance. The method includes exciting the transmit circuit with the first voltage signal.

CROSS REFERENCE TO RELAYED APPLICATIONS

Not applicable.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

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THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT

Not applicable.

BACKGROUND

Apparatus, systems and methods are described herein for providing certain properties in transmit waveforms for use by a companion receiver in determining direction of approach relative to a transmitting source.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows the components of a transmit circuit, under an embodiment.

FIG. 2 shows the components of a receive circuit, under an embodiment.

FIG. 3 shows time varying magnetic flux density generated by a current in a long wire, under an embodiment.

FIG. 4 shows time varying magnetic flux density generated by a current in a multi-turn air core loop, under an embodiment.

FIG. 5 shows time varying magnetic flux density generated by a current in a multi-turn ferrite core loop, under an embodiment.

FIG. 6 shows a loop antenna, under an embodiment.

FIGS. 7A-7C demonstrates excitation characteristics for a dominantly inductive wire load, under an embodiment.

FIGS. 8A-8C demonstrates excitation characteristics for a dominantly inductive wire load, under an embodiment.

FIGS. 9A-9C demonstrate excitation characteristics for a for a dominantly resistive long wire load, under an embodiment.

FIGS. 10A-10C demonstrate excitation characteristics for a for a dominantly resistive long wire load, under an embodiment.

FIG. 11 shows reference current I_(L) (t) resulting from the discrete time function I_(L)(nΔt), under an embodiment..

FIG. 12 shows phasor Φ(nΔt) rotating about a unit circle, under an embodiment.

FIG. 13 shows the frequency content of a desired current provided by a discrete time function, under an embodiment.

FIG. 14 shows a first carrier component of a desired current, under an embodiment.

FIG. 15 shows a second carrier component of a desired current, under an embodiment.

FIG. 16 shows a two carrier approximation of a desired current, under an embodiment.

FIG. 17 shows voltage amplitudes V_(out) and V_(C) as a function of time(seconds), under an embodiment.

FIG. 18 shows a transmit circuit, under an embodiment.

FIG. 19 shows a voltage step waveform, under an embodiment.

FIG. 20 shows a voltage signal resulting from a voltage step waveform, under an embodiment.

FIG. 21 shows a graph of an impedance vector, under an embodiment.

FIG. 22 shows a voltage signal generated by the transmit circuit, under an embodiment.

FIG. 23 shows a graph of an impedance vector, under an embodiment.

FIG. 24 shows a graph of an impedance vector, under an embodiment.

FIG. 25 shows a graph of an impedance vector, under an embodiment.

DETAILED DESCRIPTION

An electronic animal containment system is described with direction-of-approach determination, or direction-sensitive capabilities. The direction-sensitive animal containment system generally contains a transmitter unit connected to a wire loop bounding a containment area and a receiver unit carried by the animal. The transmit unit provides certain properties in transmit waveforms for use by a companion receiver in determining direction of approach relative to the wire loop bounding the containment area.

Multiple embodiments of an electronic animal containment system provide varying methods for generating the required current in the wire loop. Under one embodiment, a containment signal generator may convert an uneven duty cycle square wave into an asymmetric triangle wave. Under another embodiment, a containment signal generator includes a discrete triangle wave generator allowing the adjustment of the rising and falling slopes. Under this embodiment, the discrete triangle wave generator directly drives the output current drivers and provides two amplitude levels for the triangle waveform.

Under either embodiment, the circuit parameters, L_(total) and R_(total) determine the generating signal required to produce the desired current by the equation:

$\begin{matrix} {{V_{generator}(t)} = {{R_{total}*{I_{desired}(t)}} + {L_{total}*\frac{{dl}_{desired}(t)}{dt}}}} & (1) \end{matrix}$

A companion receiver is responsive to:

V _(receive)(t)=K _(IRx) *dβ/dt   (2)

where

dβ/dt is the rate of change of the magnetic flux density; dβ/dt is dependent upon dI(t)/dt

K _(Rx) =n*A*u _(c−Rx)

n=number of turns in the receive core

A=area of the receive core (m²)

U_(c−Rx)=geometry dependent relative permeability of the receive core

Under one embodiment of an electronic animal containment system, a containment signal generator produces an uneven duty cycle square wave. A long wire load (or perimeter boundary wire) connected to the transmitter may result in an asymmetric triangle current flowing through the wire. This is true when the load is predominantly inductive under an embodiment, hence:

$\begin{matrix} {{V_{generator}(t)} = {L_{total}*\frac{{dI}_{desired}(t)}{dt}}} & (3) \\ {\frac{{dI}_{desired}(t)}{dt} = {{V_{generator}(t)}/L_{total}}} & (4) \end{matrix}$

Under this specific condition, an uneven duty cycle square wave will produce the desired asymmetry in the wire current.

Under another embodiment, a containment signal generator includes a discrete triangle wave generator allowing the adjustment of the rising and falling slopes. The discrete triangle wave generator directly drives the output current drivers and provides two amplitude levels for the triangle waveform. However, the desired asymmetry is produced only when the load is predominantly resistive under an embodiment, hence:

V _(generator)(t)=R _(total) *I _(desired)(t)   (5)

I _(desired)(t)=V _(generator)(t)/R _(total)   (5)

Under this specific condition a discrete triangle wave generator with adjustable rising and falling slopes produce the desired asymmetry. Magnetic Field Relationships between the Transmitter and Receiver

System Model

FIG. 1 shows the components of a transmit circuit 100. FIG. 1 shows a signal generator 102 connected to an amplifier 120. The amplifier is connected to transmit components comprising resistor R_(series) 104, which is in series with inductor L_(Loop) 106, which is in series with resistor R_(Loop) 108, which is in series with resistor R_(sense) 110. The transmit components are indicated in bold as shown in FIG. 1. Current I_(L) (t) 112 flows through the transmit components. The amplifier 120 may be any amplifier topology with sufficient power output capability to produce V_(out)(t) and I_(L) (t)for the given load. Note that V_(out)(t) is given by the following equation:

V _(out)(t)=(R _(series) +R _(Loop) +R _(sense))*I _(L)(t)+L _(Loop) *dI _(L)(t)/dt.   (7)

FIG. 1 also shows analog-to-digital convertors 114 and 116 respectively connected to the transmit loop at points 118 and 120. An analog-to-digital converter (ADC) is a device that converts a continuous physical quantity (in this case, I_(L)(t) produces a voltage across R_(sense)) to a digital number that represents the quantity's amplitude. The conversion involves quantization of the input, so it necessarily introduces a small amount of error. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. The summation component 120 of the transmit circuit combines the voltage amplitude at point 118 and point 120 to approximate the voltage drop across R_(sense), i.e. V_(C)(t) 124.

FIG. 2 shows the components of a receive circuit 200. FIG. 2 shows interference 202 and time varying magnetic flux density,

$\frac{d\; \beta}{dt},$

204 presented to the receive components. V_(sensor)(t) 206 is the voltage rendered by the receive R-L-C circuit. The receive components include inductor L_(s) 208 and resistor R_(s) 210 in series. The receive components are in parallel with resistor R_(L) 212 and capacitor C_(RES) 214 which are in series with each other. The parallel circuit components are also in series with capacitor C 216. Points 220 and 222 represent respective inputs for Z Amplifier 230, Y Amplifier 240, and X Amplifier 250. VZ_(Receive)(t) 260 represents the output voltage of the Z Amplifier. VY_(Receive)(t) 270 represents the output voltage of the Y Amplifier. VX_(Receive)(t) 280 represents the output voltage of the X Amplifier. Typically, the inductors, Ls, associated with each amplifier circuit (X, Y, and Z) are oriented orthogonal to one another. Note that for the sake of simplicity, the systems and methods described below refer to a single amplifier of a receiver. V_(Rx sensor)(t) indicates the amplifier input voltage under an embodiment. V_(Receive)(t) represents amplifier output voltage.

Magnetic Field Relationships

FIG. 3 shows the time varying magnetic flux density generated by a current in a long wire. FIG. 3 shows an inductor L_(L) 302 in series with a resistor R_(L) 304 which reflect the circuit model for a long wire under an embodiment. FIG. 3 shows current I_(L) 306. The point x 308 represents the distance to the wire in meters. The point X 310 shows the magnetic flux density travelling into the page. The time varying magnetic flux density is governed by the following equations:

$u_{0} = {4\pi*10^{- 7}\left( \frac{Henry}{meter} \right)}$ I(t) = loop  current  (amps) x = distance  to  point  (meters) ${\beta (t)} = {{I_{L}(t)}\left( \frac{u_{0}}{2\pi \; x} \right)}$

The time varying flux density at point x is specifically given by

dβ/dt=dI _(L)(t)/dt*(u ₀/2πx)   (8)

FIG. 4 shows time varying magnetic flux density generated by a current in a multi-turn air core loop. FIG. 4 shows the direction of the time varying magnetic flux density 402. The multi-turn air core loop 404 comprises n turns, n_(L). Current I_(L) enters the page at points 408 and exits the page at points 406. The coil 404, i.e. each loop turn, comprises a radius r_(L) 410. The time varying magnetic flux density at a point x along the coil axis shown is governed by the following equations:

$\beta = {{I(t)}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}$ ${d\; {\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}$ I_(L)(t) = loop  current  (amps) $u_{0} = {4\pi*10^{- 7}\left( \frac{Henry}{meter} \right)}$ n_(L) = number  of  turns

The time varying flux density at point x along the coil axis is specifically given by

$\begin{matrix} {{d\; {\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}} & (9) \end{matrix}$

FIG. 5 shows time varying magnetic flux density 502 generated by a current in a multi-turn ferrite core loop 504. The ferrite core loop comprises n turns, n_(L) 506. The coil 504, i.e. each loop turn, comprises a radius r_(L) 508. FIG. 5 shows the direction of the time varying magnetic flux density 502 and direction of current I_(C) 510. The time varying magnetic flux density at a point x along the coil axis is governed by the following equations:

$\beta = {{I(t)}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}$ ${d\; {\beta/{dt}}} = {{{{dI}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}$ I_(L)(t) = loop  current  (amps) $u_{0} = {4\pi*10^{- 7}\left( \frac{Henry}{meter} \right)}$ u_(c − Tx) = 10  to  100  (typical  relative  permeability  of  the  ferritetransmitter  core  geometry  and  material) n_(L) = number  of  turns

The time varying flux density at point x along the coil axis is specifically given by

$\begin{matrix} {{d\; {\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}} & (10) \end{matrix}$

Receiver Output Voltage

Receive sensor output voltage results from proximity to a time varying magnetic flux density. FIG. 6 show an “n” turn 602 loop antenna 604 with area “A” 608. Note that the area A represents the area of one loop antenna turn. The upwardly directed arrows represent time varying magnetic flux density 610. The parameter a 620 represents the angle between horizontal line 622 and the loop antenna. The receive sensor output voltage is given by

$V_{out} = {{{- {nx}}\frac{d\; \varphi}{dt}} = {{- n}*{A({dot})}d\; {\beta/{dt}}}}$ ${{for}\mspace{14mu} {air}\mspace{14mu} {core}\text{:}\mspace{14mu} \frac{d\; \beta_{air}}{dt}} = \frac{u_{0}{dH}}{dt}$ ${{for}\mspace{14mu} {ferrite}\mspace{14mu} {core}\text{:}\mspace{14mu} \frac{d\; \beta_{FC}}{dt}} = {{u_{0}*{u_{C - {Rx}}\left( \frac{dH}{dt} \right)}} = {u_{c - {Rx}}*d\; {\beta_{air}/{dt}}}}$ u_(c − Rx) = u_(r)/(1 + N(u_(r) − 1))

Note that N is a geometry dependent demagnetizing factor, and u_(r) is the relative permeability of the receive core. A small N results in u_(c−Rx) that approaches u_(r).

This particular receiver sensor output voltage, V_(Rx Sensor) (t) is given by:

$\begin{matrix} {{V_{{Rx}\mspace{11mu} {Sensor}}(t)} = {\left( {{- n}*A*u_{c - {Rx}}} \right)*\frac{d\; \beta}{dt}}} & (11) \\ {{V_{{Rx}\mspace{11mu} {Sensor}}(t)} = {K_{Rx}*d\; {\beta/{dt}}}} & (12) \end{matrix}$

where,

K_(Rx)=−n*A*u_((C−Rx))(constant receive terms)

n=number of turns in the receive core

A=area of the receive core (m²)

u_(C−Rx)=geometry dependent relative

permeability of the receive core

As shown above, the sensor output is proportional to dβ(t)/dt. However, dβ(t)/dt is dependent on the source of the time varying magnetic field (i.e. long wire, air coil, ferrite coil, etc.)

For a long wire:

dβ/dt=dI _(L)(t)/dt*(u ₀/2πx)   (13)

dβ/dt=dI _(L)(t)/dt*K _(Tx−long wire)   (14)

where,

$u_{0} = {4\pi*10^{- 7}\left( \frac{Henry}{meter} \right)}$

x=distance to wire or loop (m)

K_(TX-long wire)=u₀/2πx

For Multi-Turn Air Core Loop:

$\begin{matrix} {{d\; {\beta/{dt}}} = {{{{dI}(t)}/{dt}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}} & (15) \\ {{d\; {\beta/{dt}}} = {{{{dI}(t)}/{dt}}*\left( K_{{Tx} - {{coil}\mspace{11mu} {air}}} \right)}} & (16) \end{matrix}$

where,

n_(L)=number of turns

r_(L)=radius of the mult turn transmit coil loop

$K_{{Tx} - {{coil}\mspace{11mu} {air}}} = {n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}$

For a Multi-Turn Ferrite Core Loop:

$\begin{matrix} {{d\; {\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}} & (17) \\ {{{d\; {\beta/{dt}}} = {{{{dI}_{L}(t)}/{dt}}*K_{{Tx} - {{coil}\mspace{11mu} {ferrite}}}}}{where}} & (18) \\ {{u_{C - {Tx}} = {{geometry}\mspace{14mu} {dependent}\mspace{14mu} {relative}\mspace{14mu} {permeability}\mspace{14mu} {of}\mspace{14mu} {the}}}\text{}{{transmit}\mspace{14mu} {core}}} & (19) \\ {K_{{Tx} - {{coil}\mspace{11mu} {ferrite}}} = {u_{c - {Tx}}*n_{L}*u_{0}*{r_{L}^{2}/\left( {2\left( {r_{L}^{2} + x^{2}} \right)^{\frac{3}{2}}} \right)}}} & (20) \end{matrix}$

The receive sensor plus amplifier output voltage, V_(Receive)(t), can be generalized as

V _(Receive)(t)=Gain_(amp)(F _(C))*V _(Rx Sensor)(t)=Gain_(amp)(F _(C))*K _(Rx) *dβ/dt   (21)

V _(Receive)(t)=Gain_(amp)(F _(C))*dI _(L)(t)/dt*K _(Rx)*(K _(Tx(#)))   (22)

where,

-   -   Gain_(amp)(F_(C))=the amplifier gain at the frequency of         interest     -   K_(Rx)=−n*A*u_(C−Rx) (constant receive terms)     -   n=number of turns in the receive core     -   A=area of the receive core (m²)     -   u_(C−Rx)=geometry dependent relative permeability of the receive         core     -   K_(Tx)(#) is dependent on the source of the time varying         magnetic field         Therefore, an observable asymmetric property in dI_(L)(t)/dt, is         preserved in V_(Receive)(t) The asymmetry may be exploited by         the companion receiver to indicate the direction of approach.

The desired transmit current contains an asymmetry in dI_(L)(t)/dt that permits a receiver to determine direction of approach. The dI_(L)(t)/dt asymmetry is observed as a difference between the positive and negative time duration and/or a difference in the positive and negative peak values at the output of the receiver sensor and amplifier chain.

FIG. 7 and FIG. 8 demonstrate excitation characteristics for a dominantly inductive wire load. FIGS. 7A-7C show an example of square wave excitation under an embodiment. FIG. 7A shows load voltage V(t) of a transmitter as a function of time (seconds). FIG. 7B displays the corresponding load current. In particular, FIG. 7B shows the filtered load current I_(L) as a function of time (seconds). FIG. 7C shows the filtered rate of change in load current dI_(L)(t)/dt as a function of time (seconds). FIGS. 8A-8C shows an example of triangle wave excitation under an embodiment. FIG. 8A shows the load voltage V(t) of a transmitter as a function of time (seconds). FIG. 8B displays the corresponding load current. In particular, FIG. 8B shows the filtered load current I_(L) as a function of time (seconds). FIG. 8C shows the filtered rate of change in load current dI_(L)(t)/dt as a function of time (seconds). Note from FIG. 7 and FIG. 8 that for dominantly inductive long wire loads, the desired asymmetry in dI_(L)(t)/dt occurs for square wave excitation.

FIG. 9 and FIG. 10 demonstrate excitation characteristics for a dominantly resistive long wire load. FIGS. 9A-9C show an example of square wave excitation under an embodiment. FIG. 9A shows load voltage V(t) of a transmitter as a function of time (seconds). FIG. 9B displays the corresponding load current. In particular, FIG. 9B shows the filtered load current I_(L) as a function of time (seconds). FIG. 9C shows the filtered rate of change in load current dI_(L)(t)/dt as a function of time (seconds). FIGS. 10A-10C show an example of triangle wave excitation under an embodiment. FIG. 10A shows the load voltage V(t) of a transmitter as a function of time (seconds). FIG. 10B displays the corresponding load current. In particular, FIG. 10B shows the filtered load current I_(L) as a function of time (seconds). FIG. 10C shows the filtered rate of change in load current dI_(L)(t)/dt as a function of time (seconds). Note from FIG. 9 and FIG. 10 that for dominantly resistive long wire loads, the desired asymmetry in dI_(L)(t)/dt occurs for asymmetric triangle wave excitation.

System, Method, and Apparatus for Constructing Voltage Excitation Waveform Discrete Time Function

Under one embodiment, a discrete time function, I_(L)(nΔt) is created which describes the desired load current asymmetry. Under an embodiment, the desired asymmetry is a triangle current waveform with different positive and negative slopes. FIG. 11 shows reference current I_(L)(t) resulting from the discrete time function I_(L)(nΔt) as further described below.

OOK (On Off Keying) or amplitude modulation (amplitude shift keying) is used to modulate (or impart data onto) the discrete time function I_(L)(nΔt) as further described below. The modulation function is referred to as modulation(nΔt) and resolves to either one or zero under an embodiment.

Rotating phasor values, expressed as Φ(nΔt)=ωnΔt (modulo 2π), are used to generate the discrete time function I_(L)(nΔt) as further described below.

The discrete time function I_(L)(nΔt) comprises a desired asymmetry of 30%. Symmetry test thresholds for Φ(nΔt) are as follows:

s₁=0.942478 radians

s₂=5.340708 radians

Using these test thresholds, the region of positive slope comprises 30% of 2π radians.

FIG. 12 shows phasor Φ(nΔt) rotating about a unit circle with a frequency, f. Note that angular frequency ω (rads/sec)=2πf. FIG. 12 shows symmetry test threshold s₁=0.942478 and s₂=5.340708. FIG. 12 displays a region of positive slope 1210 and a region of negative slope 1220 that result in the desired asymmetry.

The desired positive slope m₁ of I_(L)(nΔt) comprises change in amplitude/change in Φ(nΔt). The desired positive slope of i_(L)(nΔt) is m₁=2/(2*s₁). The desired negative slope m₂ of I_(L)(nΔt) comprises change in amplitude / change in Φ(nΔt). The desired negative slope of I_(L)(nΔt) is m₂=−2/(2π−2*s₁).

The discrete time function, I_(L)(nΔt) is given by the following logic:

if (modulation(nΔt)!=0)   (23)

-   -   if (Φ(nΔt)>=s₂ OR Φ(nΔt)<s₁), // region of positive slope         -   if (Φ(nΔt)<s₁), ΔΦ=Φ(nΔt)+s₁         -   else ΔΦ=Φ(nΔt)−s₂         -   I_(L)(nΔt)=(modulation(nΔt)*ΔΦ*m₁)−1         -   else // region of negative slope,

ΔΦ=Φ(nΔt)−s ₁

-   -   -   I_(L)(nΔt)=(modulation(nΔt)*ΔΦ*m₂)+1

else I_(L)(nΔt)=0 // no modulation

FIG. 13 shows the frequency content of the desired current provided by the discrete time function, I_(L)(nΔt), when f=20,000 Hz. FIG. 13 provides the results of Discrete Fourier Transform analysis. The figure shows a first harmonic at a frequency of 20,000 Hz and with relative amplitude 53 db. The figure shows a second harmonic at a frequency of 40,000 Hz and with relative amplitude of 43 db. The figure shows a third harmonic at a frequency of 60,000 Hz and with relative amplitude of 30 db. The relative harmonic relationships of the desired I_(L)(nΔt) are:

Harmonic: Relative Amplitude: Relative Phase (rads): 1st 1 0 2nd 0.3060 0 3rd 0.0819 0 Practical limitations of the DFT algorithm permit showing only the first three harmonics. In practice, the harmonics continue indefinitely.

Approximate Current Using First and Second Harmonics

The desired current may then be approximated using only the first and second harmonics. FIG. 14 shows a first carrier I_(FC)(nΔt) component of the desired current using the first relative amplitude of the first harmonic. FIG. 15 shows a second carrier I_(2FC)(nΔt) component of the desired current using the relative amplitude of the second harmonic. Again note that the relative amplitude of the first and second harmonics are 1.00 and 0.3060 respectively. Therefore, a two carrier approximation to (nΔt) (shown in FIG. 16) is given by

AI _(L)(nΔt)=sin(ωnΔt)+0.3060*sin(2ωnΔt)   (24)

where,

f=20,000Hz

ω=2πf

The sample rate, 1/Δt, is left to the discretion of the system designer but should be high enough (i.e. =>8× the fundamental frequency) to achieve the desired precision. The sampling rate used in this example is 160,000 Hz, i.e. 8*f. With only two terms, the operations required to realize the approximation are easy to perform in a low cost commercial microprocessor using either batch or real time processing algorithms.

Iterative, Adaptive, Feedback Control Algorithm

Derive an Estimate of the Loop Inductance (L_(Loop)) and Loop Resistance (R_(Loop))

Under one embodiment, an estimate of the loop inductance (L_(Loop)) and loop resistance (R_(Loop)) are derived. Reference is made to the transmit circuit shown in FIG. 1. The transmit circuit of FIG. 1 is excited with a reference step and the response V_(C)(t) is analyzed. FIG. 17 shows voltage amplitudes V_(out) [˜2V] and V_(C) [˜0.75V] as a function of time(seconds).

$\begin{matrix} {{V_{C}\left( {{final}\mspace{14mu} {value}} \right)} = {{V_{Out}\left( {{final}\mspace{14mu} {value}} \right)} = {R_{Sense}/\left( {R_{Sense} + R_{Loop} + R_{Series}} \right)}}} & (25) \\ {\mspace{79mu} {R_{Loop} = {{\left( \frac{V_{Out}}{V_{C}} \right)*R_{Sense}} - R_{Sense} - R_{Series}}}} & (26) \end{matrix}$

For a long wire circuit employed under the embodiment described herein, the R_(series) is in the range of 90-180 ohms and R_(sense) is 30 ohms.

Averaging multiple measurements yields a good approximation of R_(Loop) under an embodiment. The transmit loop time constant may be used to approximate the value of L_(Loop). The transmit loop time constant may be expressed as T_(C)=L/R. In one time constant T_(C)=L/R), V_(C)(t) reaches 63.2% of its final value. Under an embodiment, the elapsed time, Δt1, is recorded when V_(C)(t) reaches 63.2% of its final value. In two time constants, V_(C)(t) reaches 86.5% of its final value. Under an embodiment, the elapsed time, Δt2, is recorded when V_(C)(t) reaches 86.5% of its final value. L_(Loop) is calculated as follows:

L _(Loop) =R _(Circuit) *Δt1   (27)

L _(Loop) =R _(circuit) *Δt2/2   (28)

where R_(Circuit)=R_(series)+R_(sense)+R_(Loop). Averaging multiple measurements yields a good approximation of L_(Loop).

The measurement interval can be long (as compared to the interval between data transmissions) and left to the discretion of the system designer. In general, changes in the loop parameters (other than an open circuit) do not occur suddenly. Open circuits can be detected by observing V_(C)(t) during all other active periods.

Scale the Approximation AI_(L)(nΔt) and Calculate First Iteration of V_(Gen)(nΔt).

A working animal containment system requires a minimum receive signal at a distance x from the transmit loop. Under an embodiment, the necessary amplitude of the two carrier approximation, AI_(L)(nΔt) is calculated.

V _(Receive-required)=Gaiu_(sensor+amp)(F _(C), 2F _(C))*V _(Sensor-required)   (29)

V _(Receive-required)=Gaiu_(sensor+amp)(F _(C), 2F_(C))*ΔI _(L) /Δt _(-required) * K _(Rx) *KT _(x(#))   (30)

ΔI _(L) /Δt _(-required) =V _(Receive-required)/(Gaiu_(sensor+amp)(F _(C), 2F _(C))*K _(Rx) *K _(Tx(#)))   (31)

where,

-   -   Gain_(senor+amp)(F_(C), 2_(FC))=sensor plus amplifier gain at         the frequency or band of interest.     -   K_(Rx)=−n*A*u_(C−Rx)     -   K_(Tx(#))=is dependent on the distance, x, and the source type¹     -   Δ=the discrete time differentiation operator ¹It is either         K_(Tx-long wire), K_(Tx-coil air), or K_(Tx-coil ferrite).         Under the embodiment described below,

V_(Receive-required)˜18.6 mVRMS

Gain_(sensor+amp)(F_(C), 2F_(C))˜2550

n˜950

A˜1.164e−5 square meters

u_((c−Rx))˜5.523

The sensor plus amplifier needs to be responsive from F_(C) to 2F_(C). A relatively flat response is ideal, but other response characteristics (gain and phase) may be compensated for by digital signal processing in the receiver's microprocessor.

Under an embodiment, solve for the load current scaling factor, K_(I):

ΔI _(L) /Δt _(-required) =K _(I) *ΔAI _(L) /Δt _(-peak)   (32)

K _(I) =ΔI _(L) /Δt _(-required)/(ΔAI _(L) /Δt _(-peak)).   (33)

The resulting loop current is therefore, AI_(L)(nΔt)=K_(I)*(sin(ωnΔt)+0.3060* sin(2ωnΔt)). Under an embodiment, V_(Gen)(nΔt) is calculated using Kirchhoff s law, i.e. by

V _(Gen)(nΔt)=K ^(I)*(R _(Circuit) *AI _(L)(nΔt)+L _(Loop) *ΔAI _(L)(nΔt)/Δt)).   (34)

Under one embodiment the first iteration of the signal generator voltage waveform, V_(Gen)(nΔt), may be employed as the generator signal for system operation. One may stop here if there is high confidence the estimated loop parameters adequately reflect the circuit operating conditions for achieving the desired amplitude and asymmetry. Observe V_(C)(nΔt) for the Desired Characteristics in the Transmit Loop Current AI_(L)(nΔt)

Under an embodiment, one may observe V_(C)(nΔt) for the desired characteristics in the transmit loop current AI_(L) (nΔt). FIG. 18 shows the same transmit circuit as displayed in FIG. 1 with additional elements to model the receiver signal processing using V_(C)(nΔt). As seen in FIG. 18, the V_(C)(nΔt) signal outputs to a digital component 130 that approximates the Receiver (Rx) Sensor Response. The digital approximation is sufficiently modeled as a single pole high pass filter (f_(corner)=2525 Hz) followed by a single pole low pass filter (f_(corner)=38870 Hz) and a gain of 2550. As seen in FIG. 18, the digital approximation component 130 outputs to the Receiver (Rx) Detection Component/Algorithm 132. The receiver detection component/algorithm generates the weighted and time shifted sum of two bandpass filter outputs. One centered at the fundamental carrier frequency and one centered at 2× the fundamental carrier frequency. A relative time shift between the two filter outputs is required to match the difference in group delay through each bandpass filter. The receiver detection algorithm (also referred to as the feedback detection algorithm) estimates the root means square, V_(Rx-Rms) 134 (at the required distance measured in Analog-to-Digital-Converter counts) and Rx Asymmetry Value 136 (ratio of the aggregate negative to positive signal peaks) of the receive signal.

Under one embodiment, an adaptive feedback algorithm seeks a solution to satisfy both the minimum receive signal, V_(Receive)(nΔt), and the desired receive asymmetry. In this illustrative example, the desired receive asymmetry will be the ratio of the aggregate positive and aggregate negative peaks of V_(Receive)(nΔt)

The two frequency transmit current, AI_(L)(nΔt), can be derived from the observed V_(C)(nΔt) and R_(Sense).

AI _(L)(nΔt)=V _(C)(nΔt)/R _(Sense)   (35)

ΔAI _(L)(nΔt)/Δt=[ΔAI _(L)(nΔt)−ΔAI _(L)(nΔ(t−1))]/Δt.   (36)

The illustrative example that follows is for a long wire (approximately 2500 ft. of 16AWG wire, at an operating frequency of 25000 Hz), where:

Δβ/Δt=ΔAI _(L)(nΔt)/Δt*(u ₀/2πx)   (37)

where, x=3 meters.

The receive sensor plus amplifier output voltage, V_(Receive)(t), can be generalized as

$\begin{matrix} {{V_{Receive}(t)} = {{{{Gain}_{amp}\left( F_{C} \right)}*V_{Rx}{{Sensor}(t)}} = {{{Gain}_{amp}\left( F_{C} \right)}*K_{Rx}*d\; {\beta/{dt}}}}} & (38) \\ {\mspace{79mu} {{V_{Receive}(t)} = {{{Gain}_{amp}\left( F_{C} \right)}*\frac{{dAI}_{L}\left( {n\; \Delta \; t} \right)}{\Delta \; t}*K_{Rx}*\left( K_{{Tx}{(\#)}} \right)}}} & (39) \end{matrix}$

where,

Gain_(amp)(F_(C))=the amplifier gain at the frequency of interest

K_(Rx)=−n*A*u_(C−Rx) (constant receive terms)

n=number of turns in the receive core

A=area of the receive core (m²)

u_(C−Rx)=geometry dependent relative permeability of the receive core

K_(Tx(#)) is dependent on the source of the time varying magnetic field First, the load parameters are estimated by the previously described analysis of V_(C)(nΔt) when applying a step waveform. FIG. 19 shows a step waveform V_(GEN)(nΔt) reaching voltage of approximately 0.44 volts. FIG. 20 shows the corresponding signal V_(C)(t) reaching a voltage of approximately 1.4 volts.

R_(LOOP) and R_(CIRCUIT) values are then estimated as follows.

R_(Loop estimate)=17.568 Ω

L_(Loop estimate)=0.001382 H

R_(circuit)=R_(Series)+R_(Sense)+R_(Loop estimate)=195.393

L_(Circuit)=L_(Loop estimate)=0.001382 H

Under one embodiment, an iterative examination of V_(GEN)(nΔt) begins with feedback algorithm goals as follows.

V_(Rx-RMS) _((at required distance measured in A/D Converter counts)) =7.619+/−6.5%

Rx Asymmetry Ratio_((ratio of the aggregate negative to positive signal peaks))=1.692+/−8.55%

The signal generator transmit provides the initial V_(Gen-0)(NΔt) signal to a transmit circuit comprising starting point circuit parameters of an iterative adaptive feedback algorithm. The starting point circuit parameters, Z(0), under an embodiment are:

R_(Circuit)=195.393 Ω

L_(Loop)=0.001382 H

FIG. 21 shows the initial impedance vector Z(0).

FIG. 22 shows V_(Gen-0)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm (see FIG. 18) produces the following receive model output results for V_(Gen-0)(nΔt):

V_(Rx-Rms) estimate=8.571

Rx Asymmetry estimate=1.519

The receive signal RMS is not within the acceptable range under an embodiment. When the RMS is not within limits, a scalar gain adjustment is needed. The feedback algorithm will scale the circuit impedance vector accordingly. The scalar gain adjustment is described as follows: Scalar gain adjustment:

Z=ωL+R

Z(n)=Z(n−1)*V _(Rx-RMS goal) /V _(Rx-RMS estimate)

for this example:

R _(Circuit)(1)=195.393Ω*7.619/8.571=173.690 Ω

L _(Loop)(1)=0.001382H*7.619/8.571=0.0012285H=0.001229H

Under an embodiment, the previously iterated circuit parameters are now:

R_(Circuit)=173.6901

L_(Loop)=0.001229 H

FIG. 23 shows a graph of the impedance vector Z(1).

The V_(Gen-1)(nΔt) signal is then applied to the transmit circuit, where V_(Gen-1)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm produces the following receive model output results for V_(Gen-1)(nΔt):

V_(Rx-Rms) estimate=7.546

Rx Asymmetry estimate=1.532

The receive signal asymmetry is not within the acceptable range under an embodiment. When no gain adjustment is required and the asymmetry is not within limits, an impedance vector rotation is needed. The first rotation in an iteration sequence is assumed to be positive. The feedback algorithm will rotate the circuit impedance vector accordingly.

The Z(1) impedance vector has an angle of 48.01 degrees. There is no correlation between the asymmetry error and the proper rotation direction. Our first rotation is assumed to be positive and we rotate one-sixth (⅙) of the degrees between our current angle and 90 degrees. Hence we rotate Z(1) by 7 degrees. The new impedance vector shall have the same magnitude but at an angle of 55.01 degrees.

R(2)=Z(1)Magnitude*cosine(55.01 degrees)

ωL(2)=Z(1)Magnitude*sine(55.01 degrees)

therefore;

L(2)=ωL(2)/ω.

Note that there is nothing sacred about rotating ⅙ of the degrees between the current angle and the hard boundary (0 or 90 degrees). It is a compromise between the number of iterations required to achieve a suitable end result, and the precision of the end result.

Under an embodiment, the previously iterated circuit parameters are now:

R_(circuit)=148.884 Ω

L_(Loop)=0.001354H

FIG. 24 shows a graph of the impedance vector Z(2).

The V_(Gen-2)(nΔt) signal is then applied to the transmit circuit, where V_(Gen-2)(nΔt)=K_(I)*(R_(circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)).

The feedback detection algorithm produces the following receive model output results for V_(Gen-2)(nΔt):

V_(Rx-Rms) estimate=7.546

Rx Asymmetry estimate=1.532

The receive signal asymmetry is not within the acceptable range under an embodiment. When no gain adjustment is required and the asymmetry is not within limits, an impedance vector rotation is needed. Positive rotation did not improve the asymmetry. Therefore, a negative rotation is used. The feedback algorithm will rotate the circuit impedance vector accordingly.

The Z(2) impedance vector has an angle of 55.01 degrees. Our first rotation was assumed to be positive. It did not improve the asymmetry result, therefore we must rotate in the negative direction. Rotate one-sixth (⅙) of the degrees between our current angle and 0 degrees. Hence we rotate Z(2) by 9.71 degrees. The new impedance vector shall have the same magnitude but at an angle of 45.84 degrees.

R(3)=Z(2) Magnitude*cosine(45.84 degrees)

ωL(3)=Z(2) Magnitude*sine(45.84 degrees)

therefore;

L(3)=ωL(3)/ω

Under an embodiment, the previously iterated circuit parameters are now:

R_(circuit)=180.872 Ω

L_(Loop)=0.001186H

FIG. 25 shows a graph of the impedance vector Z(3).

The V_(Gen-3)(nΔt) signal is then applied to the transmit circuit, where V_(Gen-3)(nΔt)=K_(I)*(R_(Circuit)*AI_(L)(nΔt)+L_(Loop)*ΔAI_(L)(nΔt)/Δt)). The feedback detection algorithm produces the following receive model output results for V_(Gen-3)(nΔt):

V_(Rx-Rms) estimate=7.7092

Rx Asymmetry estimate=1.582

The receive signal RMS and asymmetry are within acceptable ranges. The adaptive feedback algorithm is complete under an embodiment. The correct circuit parameters for normal operation are:

R_(circuit)=180.872

L_(Loop)=0.001186H

Also notice that the circuit impedance vector for the 3^(rd) and final iteration is neither predominantly inductive or resistive. Therefore, the required V_(Gen-3)(nΔt) is neither an “uneven duty cycle square wave” nor a “triangle wave with adjustable slopes”.

A method is described herein that comprises describing a load current with a discrete time function. The method includes using a first frequency and a second frequency to provide an approximation of the described load current, wherein a transform applied to the discrete time function identifies the first frequency and the second frequency. The method includes estimating a loop inductance and a loop resistance of a wire loop by exciting a transmit circuit with a voltage reference step waveform, wherein the transmit circuit includes the wire loop. The method includes scaling the approximated load current to a level sufficient to generate a minimum receive voltage signal in a receiver at a first distance between the wire loop and the receiver. The method includes generating a first voltage signal using the scaled load current, the estimated loop inductance, and the estimated loop resistance. The method includes exciting the transmit circuit with the first voltage signal.

The estimating the loop inductance and the loop resistance includes under an embodiment monitoring the transmit circuit's current in response to the voltage reference step waveform.

The monitoring the transmit circuit's current includes under an embodiment capturing current amplitude as a function of time in response to the voltage reference step waveform.

The transform comprises a Discrete Fourier Transform under an embodiment. The first frequency comprises a first harmonic frequency of the described load current under an embodiment.

The second frequency comprises a second harmonic frequency of the described load current under an embodiment.

The method comprises under an embodiment generating a first carrier component of the approximated load current using the first harmonic frequency, wherein the first carrier component has a weight of one.

The method comprises under an embodiment generating a second carrier component of the approximated load current using the second harmonic frequency, wherein an amplitude of the second carrier component is weighted relative to an amplitude of the first carrier component.

The transform applied to the discrete time function used to describe the load current identifies under an embodiment the relative weight of the second carrier component.

The providing the approximation of the described load current includes summing the first carrier component and the second carrier component under an embodiment.

The approximated load current comprises a discrete time function under an embodiment.

The first voltage signal comprises a discrete time function under an embodiment.

An input to the discrete time function used to describe the load current comprises a rotating phasor under an embodiment.

The phasor value periodically rotates between 0 and 27c radians under an embodiment.

The discrete time function used to describe the load current has a first slope when the phasor value is within a first range under an embodiment.

The first slope is positive under an embodiment.

The discrete time function used to describe the load current has a second slope when the phasor value is within a second range under an embodiment.

The second slope is negative under an embodiment.

The first range comprises approximately thirty percent of 2π radians under an embodiment.

The absolute value of the first slope is greater than the absolute value of the second slope under an embodiment.

The method comprises under an embodiment reading a voltage signal at a location in the transmit circuit, wherein the voltage signal is representative of a corresponding transmit current in the transmit circuit.

The method comprises under an embodiment processing the voltage signal to estimate the receive voltage signal.

The estimating includes under an embodiment determining a root mean square (RMS) of the estimated receive voltage signal.

The estimating includes under an embodiment determining an asymmetry of the estimated receive voltage signal.

The asymmetry comprises under an embodiment a ratio of the aggregate positive and aggregate negative peaks of the estimated receive voltage signal.

The method comprises establishing a target RMS value under an embodiment.

A target RMS range comprises under an embodiment he target RMS value plus or minus a percentage.

The method of an embodiment comprises establishing a target asymmetry value.

A target asymmetry range comprises under an embodiment the target asymmetry value plus or minus a percentage.

The method under an embodiment comprises iteratively adjusting an impedance vector of the transmit circuit until the RMS and the asymmetry of estimated receive voltage signal fall within the corresponding target RMS and asymmetry ranges, wherein the impedance vector initially comprises the loop resistance and the loop inductance.

The adjusting comprises under an embodiment scaling the impedance vector when the RMS falls outside the target RMS range.

The adjusting comprises under an embodiment rotating a phase angle of the impedance vector when the asymmetry falls outside the target asymmetry range.

The rotating the phase angle comprising under an embodiment a negative rotation.

The rotating the phase angle comprises under an embodiment a positive rotation.

The described load current comprises an asymmetry under an embodiment.

The receiver exploits under an embodiment the asymmetry to determine the receiver's direction of approach to the wire loop carrying the described load current.

Computer networks suitable for use with the embodiments described herein include local area networks (LAN), wide area networks (WAN), Internet, or other connection services and network variations such as the world wide web, the public internet, a private internet, a private computer network, a public network, a mobile network, a cellular network, a value-added network, and the like. Computing devices coupled or connected to the network may be any microprocessor controlled device that permits access to the network, including terminal devices, such as personal computers, workstations, servers, mini computers, main-frame computers, laptop computers, mobile computers, palm top computers, hand held computers, mobile phones, TV set-top boxes, or combinations thereof. The computer network may include one or more LANs, WANs, Internets, and computers. The computers may serve as servers, clients, or a combination thereof.

The apparatus, systems and methods for generating voltage excitation waveforms can be a component of a single system, multiple systems, and/or geographically separate systems. The apparatus, systems and methods for generating voltage excitation waveforms can also be a subcomponent or subsystem of a single system, multiple systems, and/or geographically separate systems. The components of the apparatus, systems and methods for generating voltage excitation waveforms can be coupled to one or more other components (not shown) of a host system or a system coupled to the host system.

One or more components of the apparatus, systems and methods for generating voltage excitation waveforms and/or a corresponding interface, system or application to which the apparatus, systems and methods for generating voltage excitation waveforms is coupled or connected includes and/or runs under and/or in association with a processing system. The processing system includes any collection of processor-based devices or computing devices operating together, or components of processing systems or devices, as is known in the art. For example, the processing system can include one or more of a portable computer, portable communication device operating in a communication network, and/or a network server. The portable computer can be any of a number and/or combination of devices selected from among personal computers, personal digital assistants, portable computing devices, and portable communication devices, but is not so limited. The processing system can include components within a larger computer system.

The processing system of an embodiment includes at least one processor and at least one memory device or subsystem. The processing system can also include or be coupled to at least one database. The term “processor” as generally used herein refers to any logic processing unit, such as one or more central processing units (CPUs), digital signal processors (DSPs), application-specific integrated circuits (ASIC), etc. The processor and memory can be monolithically integrated onto a single chip, distributed among a number of chips or components, and/or provided by some combination of algorithms. The methods described herein can be implemented in one or more of software algorithm(s), programs, firmware, hardware, components, circuitry, in any combination.

The components of any system that include the apparatus, systems and methods for generating voltage excitation waveforms can be located together or in separate locations. Communication paths couple the components and include any medium for communicating or transferring files among the components. The communication paths include wireless connections, wired connections, and hybrid wireless/wired connections. The communication paths also include couplings or connections to networks including local area networks (LANs), metropolitan area networks (MANs), wide area networks (WANs), proprietary networks, interoffice or backend networks, and the Internet. Furthermore, the communication paths include removable fixed mediums like floppy disks, hard disk drives, and CD-ROM disks, as well as flash RAM, Universal Serial Bus (USB) connections, RS-232 connections, telephone lines, buses, and electronic mail messages.

Aspects of the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods described herein may be implemented as functionality programmed into any of a variety of circuitry, including programmable logic devices (PLDs), such as field programmable gate arrays (FPGAs), programmable array logic (PAL) devices, electrically programmable logic and memory devices and standard cell-based devices, as well as application specific integrated circuits (ASICs). Some other possibilities for implementing aspects of the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods include: microcontrollers with memory (such as electronically erasable programmable read only memory (EEPROM)), embedded microprocessors, firmware, software, etc. Furthermore, aspects of the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods may be embodied in microprocessors having software-based circuit emulation, discrete logic (sequential and combinatorial), custom devices, fuzzy (neural) logic, quantum devices, and hybrids of any of the above device types. Of course the underlying device technologies may be provided in a variety of component types, e.g., metal-oxide semiconductor field-effect transistor (MOSFET) technologies like complementary metal-oxide semiconductor (CMOS), bipolar technologies like emitter-coupled logic (ECL), polymer technologies (e.g., silicon-conjugated polymer and metal-conjugated polymer-metal structures), mixed analog and digital, etc.

It should be noted that any system, method, and/or other components disclosed herein may be described using computer aided design tools and expressed (or represented), as data and/or instructions embodied in various computer-readable media, in terms of their behavioral, register transfer, logic component, transistor, layout geometries, and/or other characteristics. Computer-readable media in which such formatted data and/or instructions may be embodied include, but are not limited to, non-volatile storage media in various forms (e.g., optical, magnetic or semiconductor storage media) and carrier waves that may be used to transfer such formatted data and/or instructions through wireless, optical, or wired signaling media or any combination thereof. Examples of transfers of such formatted data and/or instructions by carrier waves include, but are not limited to, transfers (uploads, downloads, e-mail, etc.) over the Internet and/or other computer networks via one or more data transfer protocols (e.g., HTTP, FTP, SMTP, etc.). When received within a computer system via one or more computer-readable media, such data and/or instruction-based expressions of the above described components may be processed by a processing entity (e.g., one or more processors) within the computer system in conjunction with execution of one or more other computer programs.

Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in a sense of “including, but not limited to.” Words using the singular or plural number also include the plural or singular number respectively. Additionally, the words “herein,” “hereunder,” “above,” “below,” and words of similar import, when used in this application, refer to this application as a whole and not to any particular portions of this application. When the word “or” is used in reference to a list of two or more items, that word covers all of the following interpretations of the word: any of the items in the list, all of the items in the list and any combination of the items in the list.

The above description of embodiments of the apparatus, systems and methods for generating voltage excitation waveforms is not intended to be exhaustive or to limit the systems and methods to the precise forms disclosed. While specific embodiments of, and examples for, the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the systems and methods, as those skilled in the relevant art will recognize. The teachings of the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods provided herein can be applied to other systems and methods, not only for the systems and methods described above.

The elements and acts of the various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the apparatus, systems and methods for generating voltage excitation waveforms and corresponding systems and methods in light of the above detailed description. 

We claim:
 1. A method comprising, describing a load current with a discrete time function; using a first frequency and a second frequency to provide an approximation of the described load current, wherein a transform applied to the discrete time function identifies the first frequency and the second frequency; estimating a loop inductance and a loop resistance of a wire loop by exciting a transmit circuit with a voltage reference step waveform, wherein the transmit circuit includes the wire loop; scaling the approximated load current to a level sufficient to generate a minimum receive voltage signal in a receiver at a first distance between the wire loop and the receiver; generating a first voltage signal using the scaled load current, the estimated loop inductance, and the estimated loop resistance; exciting the transmit circuit with the first voltage signal.
 2. The method of claim 1, wherein the estimating the loop inductance and the loop resistance includes monitoring the transmit circuit's current in response to the voltage reference step waveform.
 3. The method of claim 2, wherein the monitoring the transmit circuit's current includes capturing current amplitude as a function of time in response to the voltage reference step waveform.
 4. The method of claim 1, wherein the transform comprises a Discrete Fourier Transform.
 5. The method of claim 1, wherein the first frequency comprises a first harmonic frequency of the described load current.
 6. The method of claim 5, wherein the second frequency comprises a second harmonic frequency of the described load current.
 7. The method of claim 6, comprising generating a first carrier component of the approximated load current using the first harmonic frequency, wherein the first carrier component has a weight of one.
 8. The method of claim 7, comprising generating a second carrier component of the approximated load current using the second harmonic frequency, wherein an amplitude of the second carrier component is weighted relative to an amplitude of the first carrier component.
 9. The method of claim 8, wherein the transform applied to the discrete time function used to describe the load current identifies the relative weight of the second carrier component.
 10. The method of claim 8, wherein the providing the approximation of the described load current includes summing the first carrier component and the second carrier component.
 11. The method of claim 1, wherein the approximated load current comprises a discrete time function.
 12. The method of claim 1, wherein the first voltage signal comprises a discrete time function.
 13. The method of claim 1, wherein an input to the discrete time function used to describe the load current comprises a rotating phasor.
 14. The method of claim 13, wherein the phasor value periodically rotates between 0 and 2π radians.
 15. The method of claim 14, wherein the discrete time function used to describe the load current has a first slope when the phasor value is within a first range.
 16. The method of claim 15, wherein the first slope is positive.
 17. The method of claim 15, wherein the discrete time function used to describe the load current has a second slope when the phasor value is within a second range.
 18. The method of claim 15, wherein the second slope is negative.
 19. The method of claim 15, wherein the first range comprises approximately thirty percent of 2π radians.
 20. The method of claim 19, wherein the absolute value of the first slope is greater than the absolute value of the second slope.
 21. The method of claim 1, comprising reading a voltage signal at a location in the transmit circuit, wherein the voltage signal is representative of a corresponding transmit current in the transmit circuit.
 22. The method of claim 21, comprising processing the voltage signal to estimate the receive voltage signal.
 23. The method of claim 22, the estimating including determining a root mean square (RMS) of the estimated receive voltage signal.
 24. The method of claim 23, the estimating including determining an asymmetry of the estimated receive voltage signal.
 25. The method of claim 24, wherein the asymmetry comprises a ratio of the aggregate positive and aggregate negative peaks of the estimated receive voltage signal.
 26. The method of claim 24, comprising establishing a target RMS value.
 27. The method of claim 26, wherein a target RMS range comprises the target RMS value plus or minus a percentage.
 28. The method of claim 27, comprising establishing a target asymmetry value.
 29. The method of claim 28, wherein a target asymmetry range comprises the target asymmetry value plus or minus a percentage.
 30. The method of claim 29, comprising iteratively adjusting an impedance vector of the transmit circuit until the RMS and the asymmetry of estimated receive voltage signal fall within the corresponding target RMS and asymmetry ranges, wherein the impedance vector initially comprises the loop resistance and the loop inductance.
 31. The method of claim 30, the adjusting comprising scaling the impedance vector when the RMS falls outside the target RMS range.
 32. The method of claim 30, the adjusting comprising rotating a phase angle of the impedance vector when the asymmetry falls outside the target asymmetry range.
 33. The method of claim 32, the rotating the phase angle comprising a negative rotation.
 34. The method of claim 32, the rotating the phase angle comprising a positive rotation.
 35. The method of claim 1, wherein the described load current comprises an asymmetry.
 36. The method of claim 35, wherein the receiver exploits the asymmetry to determine the receiver's direction of approach to the wire loop carrying the described load current. 